On the range and kernel of Toeplitz and little Hankel operators
In this paper we study the interplay between the range and kernel of Toeplitz and little Hankel operators on the Bergman space. Let T_φ denote the Toeplitz operator on L^2_a(D) with symbol φ L^∞(D) and S_ψ denote the little Hankel operator with symbol ψ L^∞(D). We have shown that if Ran (T_φ) Ran (S_ψ) then φ 0 and find necessary and sufficient conditions for the existence of a positive bounded linear operator X defined on the Bergman space such that T_φ X=S_ψ and Ran (S_ψ) Ran (T_φ). We also obtain necessary and sufficient conditions on ψ L^∞(D) such that Ran (T_ψ) is closed., number=1, journal=Methods of Functional Analysis and Topology, author=Jena, P. K. and Das, N., year=2013, month=Mar., pages=55–67